a property of Extension in general, it must necessarily belong to all the extended individuals. Let us try and extricate the truth from the fallacy here. The divisibility which is predicated in general lies in the mathematical conception of Extension, involving among its terms the conception of parts, and consequently of partition or division into parts. Within this ideal region all is clear, demonstrable. The terms are expressed distinctly, and the conclusions are but restatements of the terms. Very different is the meaning of divisibility which relates to things, as complex reals, and not simply as abstract quantities. That means to separate parts from parts, a separation which destroys the whole as a particular and perceivable real, although retaining the general conception of a whole composed of such parts. When we divide 10 into 5 and 5, or a bar of iron into a heap of iron filings, we can indeed ideally recompose these parts, and conceive the parts to be the original wholes under new aspects. But this is an ideal reconstruction. The reals are so markedly different that they have lost many of the distinguishing properties of the wholes, and acquired properties not manifested by the wholes. We have only to consider how useless the heap of iron filings would be for most of the purposes to which the iron bar can be applied, and how the filings are so combustible that they spontaneously take fire in oxygen or chlorine, whereas the iron bar is only rendered incandescent by great heat, and we shall at once recognize the difference between the two reals, bar and filings. There are many ways in which the properties of a mass differ from those of its molecules; the chief of these is, that some properties are emergents, not resultants; another is, that individual effects which are neutralized or balanced in the mass become resultants in the divided mass; just as the individual action of a man is merged in the general action of the nation, becomes

prominent in the action of the parish board, and predominant in that of his family. The water-wave advances towards the shore, but the particles of this wave do not advance the whole is a moving form traversing the surface of the lake; the parts are stationary movements, oscillating to and fro about their centres. Again, the very direction of the movements is different in the wave and its parts, for the parts move in circles; they move up and down, while it moves forwards. Thus the paradox may be reconciled of a visibility emerging from invisible molecules, and divisibility being the property of a mass of indivisible molecules.

50. If we interrogate Experience, the answer is clear: Substances are divisible, i. e. separable into parts, but the divisibility is limited. It is so in two aspects, the separation is only a redistribution of the parts, a redistribution which destroys the original group without affecting the reality of the components, so that the sum total of their amounts remains constant; and if we effect a further redistribution, we are only shifting our arbitrary limit. Secondly, there are limits even to this process of shifting the limits; for since what we know as Matter has no existence isolated from Consciousness, and since Extension is one of the fundamental signatures. of Feeling, having degrees or quantities, it is clear that we can never have a perception nor a conception of Matter from which this inseparable element of limitation is eliminated. In the two aspects, therefore, positive and speculative, we must regard Matter as divisible into indivisible parts.

51. The so-called antinomy of Reason which pretends that Matter must be conceived as infinitely divisible, although infinite divisibility is unthinkable, must be rejected; it is a logical juggle, confounding operations on abstract Quantity with operations on concrete Reals.

INDESTRUCTIBILITY.

52. The preceding observations have to a great extent anticipated the line of argument applicable here. The indestructibility of Matter is now a scientific axiom; without it Science would be powerless, for Calculation would be vain. Yet it is by no means an axiom of Common Knowledge; so far from it, that, according to ordinary experience, Matter is daily destroyed, when bodies vanish from our sight and touch. This discrepancy is indeed explained by Science, and the apparent destruction is shown to be only a transformation; but the old belief still lingers in the tradition that Matter was created, and will be finally annihilated.

Here then on the one side we have a First Notion, which assuredly represents some truth of Experience, and on the other side a Conception directly at variance with it: a truth not only accepted by all scientific thinkers, but by some declared to be à priori, and in no way born in Experience. How are we to reconcile these views? By the same principle invoked in the analogous cases of penetrability and impenetrability, divisibility and indivisibility. Two very different significates are expressed by one and the same sign. The Matter which is declared to be indestructible is not the Matters known to be destructible, not the sensible substances, but their logical synthesis, or their imaginary Substratum. The sensible substances, objective groups, vanish and reappear under changing conditions. The Matter, or abstraction of these sensible Reals, the logical synthesis of these qualities. objectively viewed, is called the Matter of these Reals, the Substance of which they are the Forms; and this remains unchanged throughout their changes. This piece of wood is only a Form which vanishes when the wood is burnt into gases; but the Matter of which it was the

Form reappears under other Forms. There has been a transformation, not a destruction. The proof offered is both experimental and theoretical. Experimentally we learn that the gases which replace the wood have (or are) precisely the same sum of Force, measured in units of Weight; and they manifest those properties of Resistance, Pressure, Mobility, etc., which characterize Matter. Theoretically we learn that Matter, conceived as Existence, must be indestructible, because we are unable to conceive it passing into Nothingness. We cannot form a conception of any annihilation which is not a transformation, and therefore, since the non-existent can never be an object of Sense, it is unthinkable because unimaginable, and the indestructibility of Matter is an à priori truth.

53. Having stated the argument to the best of my ability, I will now criticise it. First note the ambiguity of saying that the idea of destruction is unthinkable, in the face of the fact that for centuries it has been thought. This has been evaded by the assertion that “ men did not really think the idea, they only thought they thought it." But this is to confound Conception with Imagination. In almost every thought, idea, conception, there are, over and above the condensed perceptions capable of definite expression in terms of Sense, elements incapable of such expression; in other words, there are sensible experiences. which can, severally or in groups, be reproduced in images ; and there are products of such experiences which cannot be reproduced in images, because they never were distinct objects of sensible perception. It is therefore quite possible to think precisely what we are unable to imagine otherwise than vaguely. My idea of the Infinite, for example, is precise, and not to be confounded with any other idea; but although I can reason on it, I am utterly incapable of imagining the Infinite. My idea of a million is definite, and not to be confounded with any other number, how

ever small the difference between the two. I reason with it, calculate with it, but can form only the vaguest image. of it. My idea of a mathematical line is sharply defined, but I am wholly unable to form a mental image of a line without breadth. Here then are three conceptions, each having its sensible basis, which basis is imaginable (namely, the sensible experiences of continuously shifting limits, of units summed, and of lines becoming fine by degrees), and a superadded element which is unimaginable, and these three products of mental processes are thinkable, although unimaginable.

54. Is the conception of Non-Existence interpretable in the same way? It is certainly not imaginable; but Hegel was only ambiguous when he said, "The Nothing exists, for it is a thought." It does not exist in the sense of being a Real which itself directly affects Feeling, but in the sense of being an idea which symbolically represents actual experiences. Not Here is the correlative of Here, Not Self of Self, Non-Existence of Existence. The sensible fact of negative experiences is generalized and expressed in the abstract symbol of Negation; and we can deal with this as with other symbols. When a man says, "There is nothing in this box," he has a perfectly definite meaning, which may be interpreted, "There is nothing which I can see or feel in the box." Corrected, and told that there is a thing in the box, namely, air, he will answer, "Very well, air, if you please; but there is nothing else." If again corrected, and told there was ether, and, besides the ether, space, he would say, “What you call space, I call nothing, what I mean by nothing is the absence of a sensible thing."

In the conception of a mathematical line there is a sensible experience and an intellectual experience or abstraction; and so in the conception of Non-Existence. By diminishing the breadth of the sensible line we can ideally